Best Known (33, ∞, s)-Nets in Base 9
(33, ∞, 81)-Net over F9 — Constructive and digital
Digital (33, m, 81)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (33, 80)-sequence over F9, using
- t-expansion [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- t-expansion [i] based on digital (32, 80)-sequence over F9, using
(33, ∞, 128)-Net over F9 — Digital
Digital (33, m, 128)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (33, 127)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 33 and N(F) ≥ 128, using
(33, ∞, 289)-Net in Base 9 — Upper bound on s
There is no (33, m, 290)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (33, 577, 290)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(9577, 290, S9, 2, 544), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4 635683 833753 094953 353143 138440 640594 392439 472256 082069 528150 244965 721489 667780 224773 578392 843351 356221 838109 572448 380342 709449 636036 772052 511641 307345 763170 778248 151144 838032 596406 410877 733154 101875 881166 239962 484824 982130 057422 910927 780003 483329 057352 896890 607357 473687 120032 304902 747579 790902 889471 277762 772500 667949 196121 951901 095814 789638 048737 607704 366202 639561 898537 777228 512445 780912 786985 980203 220709 298987 023965 808774 784653 256143 263537 201282 860183 596834 600244 654785 758581 422289 187218 611482 163009 415315 596664 787442 174917 384205 839880 470853 215773 / 109 > 9577 [i]
- extracting embedded OOA [i] would yield OOA(9577, 290, S9, 2, 544), but